Generic System Support for Deductive Program Development

We report on a case study in using logical frameworks to support the formalization of programming calculi and their application to deduction-based program synthesis. Within a conservative extension of higher-order logic implemented in the Isabelle system, we derived rules for program development that can simulate those of the deductive tableau proposed by Manna and Waldinger. We have used the resulting theory to synthesize a library of verified programs, focusing on sorting algorithms. Our experience suggests that the methodology we propose is well suited both to implement and use programming calculi, extend them, partially automate them, and even formally reason about their correctness